Nanoring as logic gate and memory mass device

We study the application of one nanoring driven by a laser field in different states of polarization in logic circuits. In particular we show that assigning boolean values to different state of the incident laser field and to the emitted signals, we can create logic gates such as OR, XOR and AND. we also show the possibility to make logic circuits such as half-adder and full-adder using one and two nanoring respectively. Using two nanorings we made tho Toffoli gate. Finally we use the final angular momentum acquired by the eelctron to store information and hence show the possibility to use and array of nanorings as a mass device.

Control of Electron Motion in a Molecular Ion: Dynamical Creation of a Permanent Electric Dipole

The dynamics of a diatomic one-dimensional homonuclear molecule driven by a two-laser field is investigated beyond the usual fixed nuclei approximation. The dynamics of the nuclei is treated by means of Newton equations of motion; the full quantum description is used for the single active electron. The first laser pulse (pump) excites vibrations of the nuclei, while the second very short pulse (probe) has the role of confining the electron around one of the nuclei. We show how to use the radiation scattered in these conditions by the molecule to achieve real-time control of the molecular dynamics.

Coherent control of a simple molecule through a strong laser

Laser Assisted Dirac Electron in a Magnetized Annulus

We study the behaviour of a charge bound on a graphene annulus under the assumption that the particle can be treated as a massless Dirac electron. The eigenstates and relative energy are found in closed analytical form. Subsequently, we consider a large annulus with radius ρ∈[5000,10,000]a0 in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radi…

Wavelets in Laser-Atoms and Molecules Interactions

REAL-TIME MONITORING OF LASER-DRIVEN MOLECULES

HARMONIC PROFILE IN MOLECULAR ION IN THE PRESENCE OF A LASER RADIATION FIELD

Nanorings driven by a laser field

We present the dynamics of an electron constrained over an 1D ring with radius of 0.142 nm driven by a laser field. The temporal evolution of the system is evaluated by a semi-analytical solution of the full quantum time dependent Schr¨odinger equation. In our calculation the gap energy between the ground and the first excited state of the nanoring is three times the photon energy laser (0.63 eV) and the laser intensity is 4·1014 W/cm2 . Our analysis is performed by considering different polarization states of the incident laser. Our attention is mainly focused on the study of the High Harmonic Generation (HHG), the energy and the angular momentum absorbed by the driven system. We observe 1…

Il Concetto di Energia fra Meccanica e Termodinamica nel Progetto Lauree Scientifiche

The influence of the quantum nature of nuclei in high harmonic generation from H+2-like molecular ions

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H2+ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of magn…

An experiment on wind energy

We discuss an experiment on wind energy performed with home-made apparatus. The experiment reproduces a laboratory windmill, which can pump water from a lower level to a higher one. By measuring the gain of the gravitational potential energy of the pumped water, one can determine the power extracted from the wind. The activity was carried out with high-school students, in the framework of the Italian National Plan for Scientific Degrees-Physics. The proposed experiment allows teachers to discuss renewable energy sources with students whose knowledge of physics is limited to mechanics. It gives students the possibility to gain experience with energy and to increase their awareness of this re…

The table top high frequency lasing device

Atomic and molecular systems, subjected to intense laser pulse, emit typical High-Order Armonic Generation (HHG) spectra. This work aims to investigate the possibility to obtain a laser device by HHG. At this end, we analyzed the emission spectra by a molecular ion driven by a linearly polarized laser field. The temporal behaviour is obtained using the Morlet wavelets transform of emission. The results show that, after filtration of the electromagnetic radiation emitted, it is possible to select a frequency which seems to have almost constant intensity and phase. This characteristic makes possible that HHG from a molecule can be used as high frequency laser fields.

Probing the Dynamics of a Molecular Ion with Laser Pulses

The dynamics of a H2+ molecular ion driven by two laser pulses separated by a time lag is studied beyond the Born-Oppenheimer approximation. The first, short, pulse prepares the molecule in some quantum state, which is probed by the second pulse. Under suitable conditions, the molecule emits a spectrum of redshifted high-order harmonics. The value of the redshift is proportional to the harmonic order and can be used as a measure of the speed of the atoms of the molecule.

Due 'paradossi meccanici' della Collezione Storica degli Strumenti di Fisica dell'Università di Palermo

Many instruments of the Historical Collection of the Physics Instruments of the University of Palermo date back to the early nineteenth century, when experimental Physics begun to be taught in university studies by using instruments and apparatuses in the classroom to illustrate the laws of Physics. Among the various instruments belonging to the Collection, there are also the so-called 'paradoxes', instruments with surprising properties that do not seem to follow the laws of Physics. In this article we analyze two 'mechanical paradoxes' of the Collection and discuss their possible educational use.

Simulazione numerica di una molecola H2 in campi laser intensi

Momentum partition between constituents of exotic atoms during laser-induced tunneling ionization

The tunneling ionization of exotic atoms such as muonic hydrogen, muonium, and positronium in a strong laser field of circular polarization is investigated, taking into account the impact of the motion of the center of mass on the the tunneling ionization dynamics. The momentum partition between the ionization products is deduced. The effect of the center-of-mass motion for the momentum distribution of the ionization components is determined. The effect scales with the ratio of the electron (muon) to the atomic core masses and is nonnegligible for exotic atoms, while being insignificant for common atoms. It is shown that the electron (muon) momentum shift during the under-the-barrier motion…

Laser driven quantum rings: one byte logic gate implementation

We study the effect of the carrier-envelope-phase (CEP) on the high harmonic generation (HHG) from a quantum ring driven by two short orthogonal lasers polarized along the x and y axes. In particular, by varying only the phase of the laser polarized along y it is possible to control the intensity of the emitted harmonics. In fact, we show that the system can efficiently emit harmonics if the laser polarized along y is small and that the cut-off of the spectra can be controlled by changing the phase or the intensity ratio between the two lasers. The wavelet analysis of the emitted harmonics and the time dependence of the angular momentum and of the energy acquired by the electron show that t…

Full Quantum Treatment of an H2+ Molecule in Presence of a Laser to Study the Nuclear Motion

High-Order Harmonic Generation from Molecules: Classical versus Quantum Effects

Wavelet analysis and HHG in nanorings: their applica-tions in logic gates and memory mass devices

We study the application of one nanoring driven by a laser field in different states of polarization in logic circuits. In particular we show that assigning Boolean values to different states of the incident laser field and to the emitted signals, we can create logic gates such as OR, XOR and AND. We also show the possibility of making logic circuits such as half-adder and full-adder using one and two nanorings respectively. Using two nanorings we made the Toffoli gate. Finally we use the final angular momentum acquired by the electron to store information and hence show the possibility of using an array of nanorings as a mass memory device.

The Emergence of Chaos in Quantum Mechanics

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schr&ouml

The emission time of harmonics emitted by a molecule

The behaviour of a one-electron, one-dimensional, asymmetric molecule driven by a laser field of intermediate intensity is studied. At the laser intensity used, the electron bounces back and forth from one atom to another undergoing repeated collisions with the nuclei. The scattered electromagnetic spectrum shows even and odd harmonics of the pump frequency. By means of a wavelet transform it is seen that the harmonics are emitted at different instants of time, corresponding to different locations of the electron. It is suggested that the emission time can be used as a tool to determine the position of the electron.

Piecewise static Hamiltonian for an atom in strong laser field

We show that it is possible to use a piecewise constant Hamiltonian to describe the main features of the dynamics of an atom interacting with a laser field. In particular we show that using this approximation we are able to give a good description of the ionization signal, of the HHG spectra and of the attosecond pulses generated by the radiating electron. Finally, we give an explicit formula to evaluate the ionization rate in the time dependent laser field. This formula, which is a generalization of the Landau formula for the ionization rate of an atom in a static electric field, fairly well reproduces the numerical ionization rates for a broad range of laser frequency and intensity. The m…

The dynamics of the electron in a homonuclear driven molecular ion

Abstract The radiation diffused by a one-dimensional homonuclear molecular ion driven by a laser field is studied as a function of the time. When the photon energy is resonant with the energy gap between the ground and the first excited state, the electronic probability density is seen to undergo slow and deep oscillations between the two nuclei. Synchronous to such oscillations, deep modulations of the emitted power are observed. The period of oscillation is of the order of 10 optical cycles. Detection of the variation in the intensity of the emitted electromagnetic spectrum therefore brings information on the position of the electron in the molecule.

High harmonics generation from structured nanorings

In this work we study the radiation diffused by a fictitious structured nanoring driven by an intense laser field. In our model we consider an electron moving through a cosine-shape potential. The results show that the ring, under particular conditions, emits a wide spectrum of harmonics.

Control of the high harmonic generation spectra by changing the molecule-laser field relative orientation

The time dependent Schrodinger equation of a homonuclear diatomic molecule in the presence of a linearly polarized laser field is numerically solved by means of a split-operator parallel code. The calculations are carried out by assuming a single active electron model with fixed nuclei; a simplified two-dimensional model of the system is used. The highly nonlinear response of the electron wave function to the laser electric field stimulates the molecule to emit electromagnetic radiation consisting of a wide plateau of odd harmonics of the laser field. It is shown that the emitted spectrum can be finely controlled by changing the angle between the laser electric field and the molecular axis;…

Evidence of Nuclear Motion in Hydrogen-like Molecules by Means of High Harmonic Generation

On the dynamics of confined particles: a laser test

Reduced dimensionality systems (RDS) are materials extending along one or two dimensions much more than the other(s). The degrees of freedom of the small dimension are not explored by the electrons since their energy is very large. The time dependent wave function of a particle in a short nanotube, taken as a paradigm of the RDS family, is calculated by solving the Klein–Gordon equation; the confining condition produces a small change in the mass of the particles and of the energy levels. These changes are of relativistic origin and therefore small, but can be measured by use of a weak resonant laser field which produces cumulative effects in the time development of the wave function. The s…

The double cone: a mechanical paradox or a geometrical constraint?

In the framework of the Italian National Plan ‘Lauree Scientifiche’ (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum and a couple of wooden rails.

Quantum Theory of a Radiating Harmonically Bound Charge

A phenomenological Hamiltonian giving the equation of motion of a non relativistic charges that accelerates and radiates is quantized. The theory is applied to the harmonic oscillator. To derive the decay time the physical parameters entering the calculations are obtained from the theory of the hydrogen atom; the agree- ment of the predicted value with the experiments is striking although the mathematics is very simple.

Chaos and nonlinearities in high harmonic generation

Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic…

High frequency lasing device by HHG

High frequency lasing device by HHG

Fluctuating laser field that induces a blueshift in harmonic generation

The spectrum of a two-level atom in the presence of a multimode laser pulse is calculated. The field is allowed to fluctuate in amplitude or in phase; the emitted spectrum has richer emission lines than in the case of the nonfluctuating field and shows peaks shifted toward the blue with respect to the traditional harmonic peaks. The position of the lines is predicted by the formula ω2n+1=(2n+1)(1+Δ)ωL with Δ being a parameter that can be found numerically. In this way the fluctuations seem to result in an effective increase of the laser frequency.

High-order-harmonic generation in dimensionally reduced systems

The time-dependent wave function of a nanoring driven by a laser field is obtained by exploiting the symmetries inherent to the system and used for studying the properties of the electromagnetic radiation emitted by the nanoring as a function of the polarization state of the laser. The diffused radiation has the characteristics of high-order-harmonic generation. For a noncircularly polarized laser field an extension of the expected cutoff position is evident, indicating that nanorings are efficient sources of radiation. The polarization state of the emitted harmonics can be opportunely controlled by varying the parameters of the pump field. The profile of the absorbed angular moment shows t…

Study of the Effects of Nuclear Motion on High Harmonic Generation in Simple Molecules

Quantum Ring in a Magnetic Field: High Harmonic Generation and NOT Logic Gate

The effect of a static magnetic field on the high harmonic generation (HHG) from a quantum ring driven by one laser polarized along the x-axis is studied. The spin polarization (Formula presented.) and the temporal emission of the harmonics are studied by varying the intensity of the magnetic field and it is shown how these results have a significant technological impact in computer technology; in fact a boolean algebra can be implemented by assigning 0 and 1 values to low and high pulse intensities of the emitted harmonics and logic gates like the NOT can be created.

High order harmonic generation: The role of the acceleration matrix elements and of the bound and continuum transitions

The electromagnetic spectrum emitted by a one-dimensional atom driven by a strong laser field is obtained by use of the acceleration form and interpreted by means of few general properties of the matrix elements of the acceleration operator. We show that the emission occurs essentially in a region near the atomic core where the acceleration is significant and we investigate the role of the various emission channels arising from interference effects between transitions involving the bare atomic levels.

High-order harmonic generation in fullerenes using few- and multi-cycle pulses of different wavelengths

We present the results of experimental and theoretical studies of high-order harmonic generation (HHG) in plasmas containing fullerenes using pulses of different duration and wavelength. We find that the harmonic cutoff is extended in the case of few-cycle pulses (3.5 fs, 29th harmonic) compared to longer laser pulses (40 fs, 25th harmonic) at the same intensity. Our studies also include HHG in fullerenes using 1300 and 780 nm multicycle (35 and 40 fs) pulses. For 1300 nm pulses, an extension of the harmonic cutoff to the 41st order was obtained, with a decrease in conversion efficiency that is consistent with theoretical predictions based on wave packet spreading for single atoms. Theoreti…

Il Laboratorio di Fisica nel Progetto "Lauree Scientifiche"

Quarta di copertina - Frutto di alcuni anni di lavoro degli autori nell'ambito del progetto "Lauree Scientifiche", il presente volume è rivolto agli studenti delle scuole secondarie e ai loro docenti con l'obiettivo di rafforzare quanto affrontato nelle lezioni in classe e stimolare la curiosità e la creatività dello studente. La prima parte introduce i concetti di base per una corretta impostazione metodologica nelle attivita' di laboratorio. Nella seconda parte sono trattati argomenti di meccanica e termodinamica volti allo studio dell'energia nelle sue diverse forme: cinetica, potenziale, termica. Infine, la terza parte raccoglie esperienze di meccanica e di termodinamica emerse durante …

Defects in quantum ring to control high-harmonic spectrum

AbstractThe high-harmonic generation from a structured quantum ring (SQR) driven by an intense laser field is presented within the single active electron approximation. The spectrum is studied by varying the symmetry of the physical system. The standard SQR (six identical and equidistant dots in a ring) presents a 60° rotational symmetry, that in this work is broken, moving or changing only one potential hole. We find that careful designed breaking of the geometrical symmetry of the SQR opens the possibility of controlling the characteristics of the harmonic lines such as intensity and polarization. HHG analysis of the emission spectrum performed through a Morlet wavelet, shows that the hig…

High-order harmonic generation via bound-bound transitions in an elliptically polarized laser field

We use a simplified five-level system to investigate the high-order harmonic generation (HHG) spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model, the Schrödinger equation is exactly analytically reduced to the system of ordinary differential equations, which is solved numerically. Studying the intensity and polarization of the emitted radiation, we find that under high laser ellipticity the harmonic emission is suppressed. However, the harmonic intensity typically depends nonmonotonously on the laser ellipticity. Such anomalous behavior is very pronounced for the resonant harmonic. We offer an explanation of this behavior based on the incr…

Harmonic generation by a simple degenerate three-level atom

Nuclear Molecular Dynamics Investigated by Using High Order Harmonic Generation Spectra

In this paper we show how it is possible to investigate the nuclear dynamics of simple molecular ions and molecules by looking at the high-order harmonic generation spectra they emit in the presence of a laser field. In particular we investigate two different effects: the presence of sidebands in the emitted spectra around the usual odd harmonics and an isotopic effect which affects the height of the plateau lines. We further study the advantages and the limitations of the semiclassical approach.

Monitoring molecular dynamics with high-order harmonic generation

A didactic experiment and model of a flat-plate solar collector

We report on an experiment performed with a home-made flat-plate solar collector, carried out together with high-school students. To explain the experimental results, we propose a model that describes the heating process of the solar collector. The model accounts quantitatively for the experimental data. We suggest that solar-energy topics should be included in school programmes to give students the opportunity to gain experience with solar energy and increase their awareness of the benefits that can be obtained from this remarkable and renewable energy source.

Harmonic Spectra in H2⁺ in the Presence of a Laser Field

HHG by a 3D-H2+ molecular ion

Graphene in strong laser field: experiment and theory

The interaction of graphene nanoparticles and strong 64 fs pulses is examined. We demonstrate high-order harmonic generation in the plasma contained in crumpled sheets of graphene. The morphological studies of the debris of ablated graphene, application of single-color and two-color pumps of graphene-containing plasma, and theoretical consideration of the high-order harmonic generation in this medium are presented.

Study of the effects of nuclear motion on High Harmonic Generation in simple molecules

Electrons on a spherical surface: Physical properties and hollow spherical clusters

We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number $N$ of electrons. The trends obtained with increasing $N$ are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic n…

Analytical wave function of an atom in the presence of a laser pulse

We study a simple model atom that has two bound states and a continuum of free states, interacting with a strong electromagnetic field. In our analysis we assume that only the continuum-continuum transitions occur- ring between degenerate free states are important for the dynamics of the atomic system; adopting this sim- plifying hypothesis, we show that it is possible to describe the time evolution of the atom by means of an infinite but discrete set of first-order differential equations describing a formal model atom that has two bound states and a degenerate quasicontinuum of states. Moreover, these equations depend on a small number of parameters of the bare atom and of the external las…

Sidebands of Harmonic Spectra in H2+ Molecule in the Presence of a Laser

Quantum correlations beyond entanglement in a classical-channel model of gravity

A direct quantization of the Newtonian interaction between two masses is known to establish entanglement, which if detected would witness the quantum nature of the gravitational field. Gravitational interaction is yet compatible also with gravitational decoherence models relying on classical channels, hence unable to create entanglement. Here, we show in paradigmatic cases that, despite the absence of entanglement, a classical-channel model of gravity can still establish quantum correlations in the form of quantum discord between two masses. This is demonstrated for the Kafri-Taylor-Milburn (KTM) model and a recently proposed dissipative extension of this. In both cases, starting from an un…

Ionization dynamics of a model molecular ion

We study the ionization dynamics of a model one-dimensional molecular ion as a function of the internuclear distance R, for different values of the laser intensity. The electron–nucleus potential is assumed to be a Poschl–Teller potential, whose parameters are chosen to have only two bare bound molecular states in the range of R considered. We describe three different theoretical approaches to study the dynamics of the system: an exact numerical, a semiperturbative and a phenomenological approach. All these approaches indicate the presence of a sharp ionization peak for a critical value of the internuclear distance, for which the energy difference between the two bound levels coincides with…

Space-time localization of the radiation emitted by an electromagnetically driven charge and the question of the position of an electron

Abstract We study the electromagnetic spectrum emitted by a free charge driven by a strong laser field in the proximity of a stationary scattering centre that acts as an accelerating third body. We show that under the most general conditions the radiation is emitted close to the scatterer and during a welldefined time interval. Thus it should be possible, at least in principle, to determine the position of the electron by observing the radiation that it is emitting.

Measurement of the Convective Heat-Transfer Coefficient

We propose an experiment for investigating how objects cool down toward the thermal equilibrium with its surrounding through convection. We describe the time dependence of the temperature difference of the cooling object and the environment with an exponential decay function. By measuring the thermal constant tau, we determine the convective heat-transfer coefficient, which is a characteristic constant of the convection system.

A paradigm of fullerene

We study the dynamics of an electron constrained over the surface of a rigid sphere, with geometrical parameters similar to those of the C60 fullerene, embedded in a low intensity linearly polarized laser field. The model is shown to emit odd harmonics of the laser even at very low field intensity. For more intense laser fields, the spectrum presents odd harmonics and hyper-Raman lines shaped in a broad plateau. The spectrum of the model is compared to that theoretically obtained by other authors for more realistic models of C60. It is concluded that the model can be used as a paradigm for mesoscopic molecules in the fullerene family, particularly in practical applications where it is conve…

High-order harmonic emission from a three-level atom in a laser field

Abstract The spectrum emitted by a three-level atom in the presence of a weak laser field is given together with the population dynamics and the phase of the Fourier transform of the acceleration. Calculations show that the spectrum can be very different from that emitted by a two-level atom. When the trapping conditions are obtained, the coupling to the third level can result in a large change in the spectrum.

Dynamics of H2 molecule driven by an ultra-short laser field

We describe, using a semiclassical approach, the molecular dynamics of a one-dimensional H2 molecule interacting with a laser, beyond the Born–Oppenheimer approximation. We observe and discuss different molecular behaviors, such as ionization and dissociation.

A three-colour scheme to generate isolated attosecond pulses

We propose a new scheme to produce isolated attosecond pulses, involving the use of three laser pulses: a fundamental laser field of intensity I = 3.5 × 1014 W cm−2 and of wavelength λ = 820 nm, and two properly chosen weak lasers with wavelengths 1.5λ and 0.5λ. The three lasers have a Gaussian envelope of 36 fs full width at half maximum. The resulting total field is an asymmetric electric field with an isolated peak. We show that a model atom, interacting with the above-defined total field, generates an isolated attosecond pulse as short as 1/10 of a laser period, i.e. approximately 270 as.

The Study of Nuclear Motion in D2+ Molecular Ion by Using the Harmonic Spectra

Evidence of Nuclear Motion in H2-like Molecule by Means of High Order Harmonic Generation

The dynamics of hydrogen-like molecules is investigated beyond the usual fixed nuclei approximation. The nuclear motion introduces in the familiar spectrum of emitted radiation additional regular lines whose separation is essentially given by the vibrational frequency of nuclear motion. A wavelet analysis of the emitted spectrum shows that the intensity of the harmonic lines is modulated with the same period of the nuclear motion; this suggests the possibility of the real-time control of the nuclear dynamics.

CONTROL OF MOLECULAR DYNAMICS VIA PUMP PROBE LASER PULSES

Pulse-duration dependence of the isotopic effect in simple molecular ions driven by strong laser fields

In this paper we discuss isotopic effects in simple molecular ions subjected to strong laser fields. We show that the intensity of the emitted spectra strongly depends upon both the nuclear mass of the molecular ions and the laser pulse duration. In particular, for short pulse duration [up to 8 optical cycles (o.c.)], we confirm the trend described in the most studied case in which the high-order harmonic generation is more efficient for heavier isotopes; in contrast, an interesting physical phenomenon is predicted for pulses longer than 16 o.c. characterized by an inverse effect in which lighter molecular species are responsible for higher-order harmonic emission.

Evidence of Nuclear Motion in H2 Molecule through High Horder Harmonic Generation

Harmonic generation from nanorings driven by a two-color laser field

We study the high harmonic generation and the polarization of the harmonics emitted by a nanoring driven by two laser fields of angular frequency ?1 and ?2, with ?2?=?2?1, and ?1 resonant between the ground and the first excited state. We show that by varying parameters, such as laser intensity, photon energy and the delay between the two laser pulses, we can control the number of harmonics and the polarization of the radiation. In particular we show that with this choice of two-laser photon frequency rate we obtain more harmonics with respect to other configurations. We also calculated the average absorbed energy and the average angular momentum acquired by the electron as a function of th…

High-order harmonic generation via bound-bound transitions in elliptically polarized laser field

We use a 5-level system to investigate the HHG spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model the Schrodinger equation is numerically solved and we study the dipendence of the spectra, harmonic intensity and polarization of emitted radiation on the laser field ellipticity. Studying the intensity of the emitted radiation we find that un alsoder high laser ellipticity the harmonic emission is greatly reduced; the analysis of results shows that the harmonic intensity and the emitted radiation depend on the laser ellipticity.

Variation of physical constants and electron–positron oscillations: Zitterbewegung in a plane wave

The space and time dependence of physical constants is currently a debated issue for experimental findings, and theoretical reasons seem to indicate that this is not a mere speculative possibility. The paper provides a relativistic description of a free fermion evolving under the assumption of temporal variation of the physical constants. The assumed generalisation of the Dirac equation is particularly simple and permits a grouping of the constants in one single parameter and a consequent agile treatment of the problem. The form of the equations suggests a rescaling of the temporal coordinate $$x^0=ct$$ which allows a plane wave solution. Two are the main results of the treatment. First, th…

Laser Pulse Effects in Two-level Systems Driven by Coherent and Fluctuating Radiation Fields

Abstract We reconsider the problem of a two-level system interacting with a radiation field in order to study some new features suggested by the actual experimental conditions. Pulse shape and duration effects are included in the formalism and the counter-rotating terms are retained. The criterion of validity of the rotating wave approximation (RWA) for pulsed fields is investigated; generalizing results well known in RWA, we establish some new formal results, including non-RWA contributions to all orders and for any pulse shape. The analysis is then carried out for fluctuating fields, by developing a method based on the theory of multiplicative stochastic differential equations. For short …

'Naughty cylinder' mechanical paradox

High Order Harmonics from a Molecule: Evidence of the Nuclear Motion

The electromagnetic spectrum emitted by a molecule driven by a laser presents harmonics and satellite lines whose separation is equal to the oscillation frequency of the nuclei. Full quantum and semiclassical calculations are presented.

Constraints on the spatial variation of Planck constant

AbstractInspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of$$\hbar $$ħupon the position. The protocols, both within today state of art, involve the use of two delayed laser pulses driving an atom. The distinct positions of the laboratory, due to the Earth motion, affects$$\hbar $$ħand hence the atomic dynamics. The first protocol measures the difference in population of the atomic ground state while the second one the red-shift of the harmonics emitted by the atom in the two moments of the experiment. The protocols improve the reported upper limit of$$\varDelta \hbar /\hbar $$Δħ/ħ. The theory shows that$$\hbar (\varvec{r…

Dynamic clock generator and memory mass device using a quantum ring driven by three-color laser fields

We study the behaviour and applications of a quantum ring (QR) under a three-color laser field. In particular we study the emission of harmonics and their temporal evolution through wavelets. These results suggest the use of QR for three important applications: (1) generation of single short pulses, (2) creation of a variable clock generator, (3) a memory mass device through the angular momentum acquired by the electron.

Properties of the radiation Emitted by a Laser driven quantum Ring

We present the electromagnetic emission from one electron confined in a quantum ring driven by an intense laser field. We consider both a plain ring and one structured by six potential wells that produce a static tangential force. Through a suitable one-dimensional model we numerically solve the associated Schroedinger equation obtaining the correspondent time evolution of the wave-function. We show that the emission is formed by a wide plateau that can be both quasi-continuum or resolved in discrete lines. We study the dependence of the emitted spectra from the polarization status of the external laser field and in particular we concentrate on the intensity of the emitted lines and of thei…

High harmonic generation from structured nanorings

Confinement and high-order harmonic generation by a repulsive potential

The dynamics of an electron wave packet in the presence of laser radiation and of a one-dimensional repulsive soft-core potential is investigated. For different laser intensities and for different initial positions of the electron wave packet, these results are compared with those for an attractive potential. The repulsive potential is capable of confining the electron quite efficiently under appropriate conditions. In these conditions, the electron is shown to emit a high harmonic spectrum similar to that emitted by the more conventional attractive potential. It is thus argued that recombination into an atomic bound state as required by the three step model is not essential for the emissio…

Use of three detuned lasers to generate isolated attosecond pulses

The dynamics of a one-dimensional atom driven by three-laser fields is investigated. The total electric field is made up of a fundamental laser field of intensity  W cm−2 and wavelength λ = 820 nm and two weak lasers with larger wavelengths. The intensity of the two weak fields is with k = 0.25. The frequencies of the weak fields are and , with and . The three lasers have a Gaussian envelope of 72 fs FWHM. It is shown, by numerical computation and using the semiclassical theory of high-harmonic generation, that the atom interacting with this combined field is able to emit an isolated attosecond burst of radiation.

CO2 degassing at La Solfatara volcano (Phlegrean Fields): Processes affecting and of soil CO2

Abstract The soil CO2 degassing is affected by processes of isotope exchange and fractionation during transport across the soil, which can deeply modify the pristine isotope composition. This has been observed in the Solfatara volcano, upon a field survey of 110 points, where the CO2 flux was measured, together with temperature, CO2 concentration and oxygen and carbon isotopes within the soil. Furthermore, in some selected sites, the measurements were made at different depths, in order to analyze vertical gradients. Oxygen isotope composition appears controlled by exchange with soil water (either meteoric or fumarolic condensate), due to the fast kinetic of the isotopic equilibrium between …

Electron Angular Distribution in Laser-Assisted X-ray Photoeffect

Calculations are reported of the differential cross section of the laser-assisted X-ray photoeffect from K shells showing that drastic changes occur in the shape of the ejected-electron angular distribution when laser photons are exchanged during the ionisation. This process appears well suited to the study of laser effects and multiphoton exchanges in laser-assisted atomic collisions.

Spectrum emitted by a trapped electron

We study the behaviour of a homonuclear molecule driven by an intense laser field. Newton's laws are used to describe the dynamics of nuclei while the quantal approach is reserved to the study of the electron. It is observed that the nuclei can oscillate or dissociate according to the degree of ionization of the molecule. In case of low ionization rate it is shown that great amount of information can be obtained by using the simplified approaches of fixed nuclei and of two-state approximation. Under suitable conditions the electron wave function spends a long time localized around one nucleus. The harmonic generation of the molecule is studied and seen to contain even harmonics.

Piano Nazionale Lauree Scientifiche – Fisica: un percorso di laboratorio sulle tematiche energetiche

Il terremoto avvenuto in Giappone l'11 Marzo del 2011 ha riaperto il dibattito sull'energia quale elemento centrale di sviluppo della societa' moderna. L'esperienza didattica su tematiche energetiche, maturata a Palermo nell'ambito del Piano Nazionale Lauree Scientifiche - Fisica (PLS-Fisica), si inserisce in questo contesto. Noi proponiamo un percorso formativo di laboratorio riguardante tematiche energetiche, al fine di stimolare i docenti di fisica a portare in aula e in laboratorio questi argomenti e contribuire cosi' ad aumentare la consapevolezza che gli studenti hanno riguardo alle fonti energetiche rinnovabili, ma anche riguardo alle fonti basate sui combustibili fossili e nucleari.…

A new spectroscopic technique to monitor the molecular axis orientation

Laser Assisted Atomic Ionization by a Short XUV Pulse

We report on numerical results of energy spectra of photoelectrons emitted by irradiating an hydrogen atom with a relatively weak single attosecond XUV pulse in the presence of a two-color IR laser pulse. The densities of probabilities have been obtained by treating the interaction of the atom with the XUV radiation at the first order of the time-dependent perturbation theory and describing the emitted electron through the Coulomb-Volkov wavefunction. The results of the calculations agree with the ones found by numerically solving the time-dependent Schrödinger equation. Specifically, we use an algorithm that implements an high recision variant of the Cranck Nicolson integration method and …

Attivita' del Progetto Lauree Scientifiche-Fisica dell'Ateneo di Palermo

Modello numerico tridimensionale di uno ione H2+ in campi laser intensi

Laser driven structured quantum rings

In this work we study harmonic emission from structured quantum rings (SQRs). In SQRs, electrons trapped in two-dimensional structures are further confined by an external potential composed of N scattering centers arranged on a circle. We build a suitable one-dimensional model Hamiltonian describing this class of systems and analytically solve the associated Schödinger equation. We find that the solution can be expressed in terms of Mathieu functions and focus on the specific case of N = 6. By exactly solving the time-dependent Schödinger equation, we then show how the harmonic response to linearly polarized lasers strongly depends on the ring physical parameters. The results illustrate how…

Classical chaos and harmonic generation in laser driven nanorings

A quantum ring driven by an intense laser field emits light in the form of high-harmonic radiation resulting from the strong acceleration experienced by the active electrons forced to move on a curved trajectory. The spectrum of the emitted light is rich and strongly dependent on the parameters of the problem. In order to investigate the physical origin of such variability, we focus on the seemingly simple problem of a laser-driven charge constrained to a ring from a classical standpoint. As it turns out, the dynamics of such a classical electron is governed by a nonlinear equation which results into a chaotic motion - by nature depending on the initial conditions in an unpredictable way. O…

Electron and nuclear dynamics of a molecular ion in an intense laser field

The dynamics of a two-dimensional $\mathrm{H}_{2}^{+}$ molecule interacting with a strong laser pulse beyond the usual approximation of fixed nuclei is presented. The motion of the nuclei is studied by using the classical Newton laws while the electron is described with a full quantal treatment. The axis of the molecule, initially not aligned to the laser field, performs a long-period pendular motion around the laser polarization axis. Vibrational degrees of freedom are seen to be excited. The radiation emitted by the oscillating charges presents variations that are synchronous to the pendular motion. The possibility of monitoring the motion of the molecule through the emitted radiation is …

Generation of isolated attosecond pulses using unipolar and laser fields

A new scheme to generate isolated attosecond pulses is presented that involves the use of a laser field and of a unipolar field. The laser field has a pulse of intensity I = 1.5×1014 W cm−2 and wavelength λ = 820 nm. The unipolar pulse is an asymmetric pulse consisting of a sharp peak, lasting approximately half a laser period, i.e. nearly 1.4 fs, followed by a long and shallow tail. We show that on combining these two fields, it is possible to generate isolated attosecond pulses as short as 1/10 of a laser period, i.e. approximately 270 as. Moreover, it is argued that this scheme is robust either against small variations of the laser envelope, or against small changes in the delay between …

Signature of Nuclear Motion in H2 by Menas of High Harmonic Generation

The influence of the quantum nature of nuclei in high harmonic generation from H$_2^+$-like molecular ions

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H$_2^+$ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of …

The electron wavefunction in laser-assisted bremsstrahlung

The active region for emission of radiation by an electron driven by a strong laser field in the proximity of a stationary scattering centre is localized in space and time. It is argued that the extension of this region can be controlled by changing the velocity of the electron, and that information on this extension is contained in the duration and in the spectrum of the emitted radiation pulse.

The two-level atom in high-order harmonic generation

Polarization of high harmonic generated spectra in ion

We study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as function of the angle $\theta$ between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs $\theta$ in the first or second half of the emitted spectrum. In particular, the differences are accentuated for $0^\circ < \theta < 50^\circ$, while for higher angles, until t…

Bremsstrahlung from a repulsive potential: attosecond pulse generation

The collision of an electron against a repulsive potential in the presence of a laser field is investigated. It is found that a sufficiently strong laser field forces the electron to remain in the neighbourhood of the repulsive potential causing bremsstrahlung. By appropriately filtering the emitted signal, an electron in the presence of a repulsive potential is capable of generating attosecond pulses.

Direct theoretical evidence of nuclear motion in H+2by means of high harmonic generation

The numerical solution of the time-dependent Schro ̈dinger equation for vibrating hydrogen molecular ions in many-cycle laser pulses shows that high- order harmonic generation is sensitive to laser-induced molecular vibrations. In particular, the odd harmonic lines in the emitted spectra are surrounded by additional regular peaks whose spacing is given by the vibrational frequency of the nuclei motion. Analytical theory relates these satellite peaks to the molecular vibrations in terms of an approximated effective potentials. These results are not affected by the dimensionality of the system.

Photoelectric effect from a metal surface: a revisited theoretical model

The Sommerfeld model extended to include radiation–electron interaction in the regime of highly intense fields is taken as the basis for studying theoretically the laser multiphoton photoelectric effect from a metal surface. Numerical analysis is carried out without approximations other than those inherent in the model itself; the study of the multiphoton aspect of the problem is based on a scheme that is nonperturbative in an essential way. The numerical analysis facilitates insight into the potential and the limits of the model in the interpretation of recent experiments and into the similarities and differences between the metal multiphoton effect and atomic multiphoton ionization. The r…

Two-electron systems in strong laser fields

In this paper we investigate the single and double ionization signals of ${\text{H}}_{2}$ molecules, with fixed and moving nuclei, as a function of laser intensity, for two different values of laser wavelength ($\ensuremath{\lambda}=390\text{ }\text{nm}$ and $\ensuremath{\lambda}=780\text{ }\text{nm}$), using an approach for evaluating the ionization signals which allows the investigation of relatively long-lasting pulses. The He system is first investigated to benchmark our calculation against already known results. We confirm the evidence of nonsequentiality in the ionization processes of all the systems investigated. Furthermore, we show that the nuclei motion enhances the double ionizat…

Ionization and Dissociation Dynamic of H2 Molecule Driven by a Laser Field

We study the single and double ionization yields and the dissociation dynamics of a onedimensional two-electron molecule exposed to an intense laser pulse. The double ionization yields are systematically investigated for both fixed and moveable nuclei. At low intensities the ionization curves have a power law shape, followed by a knee profile for higher intensities. A temporal correlation between the nuclear motion and the electron ionization shows that the nuclear motion deeply affects the ionization yield.

ALIGNEMENT AND REAL TIME MONITORING OF MOLECULAR IONS IN THE PRESENCE OF A LASER FIELD

Three-Dimensional Numerical Model of an H2+ Ion in Intense Laser Fields

Even harmonics from laser driven homonuclear molecules

The dynamics of a homonuclear diatomic molecule driven by a laser pulse is obtained beyond the fixed nuclei approximation. Laser parameters can be adjusted to confine the electron over one of the two nuclei for a relatively long time or not. A time-resolved analysis of the electromagnetic spectrum emitted by the molecule presents the usual odd harmonics far from confinement and even harmonics during the confinement periods. A physical interpretation of the results is given.

Transitions in Presence of Short Laser Pulses

Accurate numerical calculations are carried out to investigate the validity of the two-state approximation in the case of resonant interactions between electromagnetic radiation and atoms . Short pulses are considered and the presence of the atomic spectrum is modelled by introducing a third, nonresonant, state . We show that the harmonics of the pulse profile may play a significant role in the dynamics of the process and may cause energy nonconserving transitions between the atomic states. © 1990 Taylor & Francis Ltd.

High Order Harmonic Generation: a Tool to Monitor Molecular Dynamics

Rescattering and vibrations in homonuclear diatomic molecules in a strong electromagnetic field

Abstract The electron of a H 2 + driven by a strong electromagnetic field induces molecular vibrations. Numerical and analytical results show that the molecule behaves as a parametric oscillator and can be treated as a kicked oscillator. The results are discussed from the point of view of the electron's periodic dressing and undressing processes.

CO2 degassing at La Solfatara volcano (Phlegrean Fields): Processes affecting d13C and d18O of soil CO2

Abstract The soil CO2 degassing is a ected by processes of isotope exchange and fractionation during transport across the soil, which can deeply modify the pristine isotope composition. This has been observed in 10 the Solfatara volcano, upon a eld survey of 110 points, where the CO2 ux was measured, together with temperature, CO2 concentra- tion and oxygen and carbon isotopes within the soil. Furthermore, in some selected sites, the measurements were made at di erent depths, in order to analyze vertical gradients. Oxygen isotope composition 15 appears controlled by exchange with soil water (either meteoric or fumarolic condensate), due to the fast kinetic of the isotopic equilib- rium betw…

Quantum ring: HHG spectrum control

Atoms, molecules , clusters and other systems driven by a strong laser field of frequency \omega_L can emit a spectrum of laser harmonics. The high harmonics generation (HHG) phenomen is strongly affected by the symmetries of the system. It is well known that systems with rotational symmetries emit only odd harmonics. Numerous researcher make mainly attention to the possibilities to set different initial conditions in order to control the spectrum. Recently, the study of nanotechnology is hot-topics and in particular the study of very symmetric systems such as fullerene, nanoring and structured nanoring (nanoring with identical and symmetric scattering centers). Therefore, it is natural and…

Nanoring as logic gate and memory mass device - Poster

Polarization of high harmonic generated spectra in H+2ion

AbstractWe study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as a function of the angle between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs in the first or second half of the emitted spectrum. In particular, the differences are accentuated for , while for higher angles, until the perpendicular orientation, almost …

COS-B Observations of Long Term Variability and Absorption Phenomena in the X-ray Emission from Cen X-3

The COS-B satellite has observed the X-ray source Cen X-3 in the energy range 2 to 12 keV

H2 Molecule Driven by a Laser Field

We study the single and double ionization yields and the dissociation dynamics of a one-dimensional two-electron molecule exposed to a laser pulse of intensity IL in the range 1013 − 1015 W/cm2 and photon energy hω¯L =3.18 eV. The calculations are carried out in the case of both fixed and movable nuclei. At low IL the ionization curves have a power law shape In that is interrupted by a knee at higher intensity.

Progetto Lauree Scientifiche-Fisica dell'Ateneo di Palermo